What is (\partial)/(\partial y)(e^{3x-y^2}) ?

The answer to (\partial)/(\partial y)(e^{3x-y^2}) is -2e^{3x-y^2}y

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(\partial)/(\partial y)(e^{3x-y^2})

\frac{\partial}{\partial y} (e^{3 x - y^{2}})

- 2 e^{3 x - y^{2}} y

Solution steps

\frac{\partial}{\partial y} (e^{3 x - y^{2}})

Treat

x

as a constant

Apply the chain rule:

e^{3 x - y^{2}} \frac{\partial}{\partial y} (3 x - y^{2})

= e^{3 x - y^{2}} \frac{\partial}{\partial y} (3 x - y^{2})

\frac{\partial}{\partial y} (3 x - y^{2}) = - 2 y

= e^{3 x - y^{2}} (- 2 y)

Simplify

= - 2 e^{3 x - y^{2}} y

\frac{d ^{2}}{d x ^{2}} (\frac{x}{e ^{x}})

\frac{d}{d x} (arccos (e^{5 x}))

\int_{- 3}^{3} (16 - x^{2}) - (x^{2} - 2) d x

y = 2 sec (x) - csc (x)

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e - y

What is (\partial)/(\partial y)(e^{3x-y^2}) ?
The answer to (\partial)/(\partial y)(e^{3x-y^2}) is -2e^{3x-y^2}y